This is the middle Hardmode ore, and its first job is the anvil. Until you have smelted enough for one, almost nothing in the Hardmode crafting tree will open up for you, so the earliest bars should go there before you start thinking about armor or a better pickaxe.

against its counterpart

A world generates this or Mythril, not both, and the two sit close enough in power that the roll rarely decides a playthrough. The armor built here trades a little defense for a critical strike bonus and drops damaging flower petals onto whatever you hit, which favors fast weapons that connect often over slow heavy swings. If your world handed you the other ore, nothing is lost. The difference shows up in how the set plays, not in how strong it is.